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lfunc_lfunctions • Show schema
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{'Lhash': '2202621342870533792997946342872', 'a10': [-3.2613872124741694, -1.8829627850535648], 'a2': [-3.0590716208171305, 1.766155823749115], 'a3': [0.0, 0.0], 'a4': [4.23861278752583, -7.341492701605885], 'a5': [0.5330681358161528, 0.9233010951296033], 'a6': [0.0, 0.0], 'a7': [0.47722557505166113, 0.0], 'a8': [0.0, 15.814956047231945], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.6594125205610775, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [6.522774424948339, -17.84526306338015]]]], 'bad_primes': [3, 19], 'central_character': '171.145', 'coefficient_field': 'CDF', 'conductor': 171, 'conductor_radical': 57, 'conjugate': '306635011719050149570480566625', 'degree': 2, 'euler_factors': [[[1.0, 0], [3.0590716208171305, -1.766155823749115], [2.0, -3.4641016151377544]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.5330681358161528, -0.9233010951296033], [-12.5, 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'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 9, 'label': '2-171-19.12-c2-0-9', 'load_key': 'CMFs-workshop', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/171/3/p/f/145/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.25551101850782365, 0.3685530450570755, 0.4684426754708316, 0.5544047094161627, 0.6249956129322999, 0.6780957757181607, 0.71101924961797, 0.7207314642736884, 0.7041597273759193, 0.6585778068102197, 0.5820428608802685, 0.47385916670428513, 0.3350381268284024, 0.16871838381122856, -0.019495427430420622, -0.2213204231836568, -0.4257555622544918, -0.6192565474677436, -0.7861596221336368, -0.9093745043811905, -0.9713474400710566, -0.9552713342204754, -0.8464924837681498, -0.6340346113549512, -0.3121333427577891, 0.11834889866759912, 0.6487730402671498, 1.2619884583538066, 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'10.81821734857478988243950292295260', '11.29823185845432265725190970006811', '12.55007602241397457517311054511275'], 'prelabel': '2-171-19.12-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.158567237905986, 'root_angle': 0.47603950664612127, 'root_number': '0.07520304377850638 + 0.9971682416756201*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.238019753323', 'prec': 47}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.73756186639596990540366529544', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.09350933367236979500708433694', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.05336319159583949890029035533', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.6594125205610775, 'bad_primes': [3, 19], 'central_character': '19.12', 'conductor': 171, 'conductor_radical': 57, 'degree': 2, 'index': 9, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/171/3/p/f/145/1'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '2-171-19.12-c2-0-9', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-171-19.12-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.158567237905986, 'root_angle': 0.23801975332306063, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '1.73756186639596990540366529544', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2202621342870533792997946342872', 'Lhash_array': ['2202621342870533792997946342872'], 'label': '2-171-19.12-c2-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/171/3/p/f/145/1'}